It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

it is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. we introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. we deal with vietoris and hausdorff continuity concepts.stability of microperiodi...

Differential phase-contrast imaging with hard x rays can have important applications in medicine, material sciences, and energy research. Phase-contrast methods based on microperiodic optics, such as shearing interferometry, are particularly attractive because they allow the use of conventional x-ray tubes. To enable shearing interferometry with x rays up to 100?keV, we propose using grazing-in...

We construct a two-sided discontinuous piecewise linear minimal valid cut-generating function for the 1-row Gomory–Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. The new function only admits piecewise microperiodic perturbations. We present an algorithm for verifying certificates of non-extremality in the form of such...

We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory–Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. This anomalous behavior results from combining features of Hildebrand’s two-sided discontinuous extreme functions and Basu–Hildebrand–Köppe’s piecewise linear extreme funct...

Three-dimensional (3D) microperiodic scaffolds of poly(2-hydroxyethyl methacrylate) (pHEMA) have been fabricated by direct-write assembly of a photopolymerizable hydrogel ink. The ink is initially composed of physically entangled pHEMA chains dissolved in a solution of HEMA monomer, comonomer, photoinitiator and water. Upon printing 3D scaffolds of varying architecture, the ink filaments are ex...

A simple optical interference method to fabricate microperiodic structures was demonstrated. Femtosecond laser pulse was split by a diffractive beam splitter and overlapped with two lenses. Temporal overlap of the split femtosecond pulses, which requires 10 mm order accuracy in optical path lengths, was automatically achieved by this optical setup. One-, two-, and three-dimensional periodic mic...

A one-dimensional pure stress initial boundary value problem of linear elastodynamics for amicroperiodic layered semi-space in which amicrostructural length is taken into account is revisited. Also, the plane stress harmonic waves propagating in a microperiodic layered infinite elastic space are discussed. It is shown that (i) for a particular system of the length and time units the transient s...

3D silk/HA microperiodic scaffolds for bone tissue engineering and angiogenesis are fabricated by direct-write assembly. This approach can be used to control filament and spacing size in the scaffold to allow investigation of the effect of scaffold architecture on osteogenesis and vessel-like structure formation from stem cells and endothelial cells.